Maths-
General
Easy

Question

Which of the following is the graph of the equation y = 3x - 2 in the x y-plane?

  1.     

hintHint:

Hint:
The graph of an equation is the representation of the equation on the xy -plane. We are given the equation of a line and we need to find its graphical representation. When a line cuts through x-axis, then the y -coordinate  is 0 and when it cuts y -axis, the x -coordinate is 0 . We use this idea to check which of the graphs in the options satisfy the given equation.

The correct answer is:


    We are given the equation y equals 3 x minus 2
    We find its x-intercept, that is, the point at which the line cuts x-axis.
    To find x-intercept, we put y = 0  in the above equation.
    So, we get
    0 = 3x - 2
    Simplifying, we get
    x equals 2 over 3
    Thus, the x-intercept is 2 over 3.
    Similarly, we find the y-intercept of the line, that is, the point at which the line cuts y-axis.
    To find the y-intercept, we put x=0 in the above equation to get
    y equals 3.0 minus 2
    Simplifying, we get
    y = - 2
    Thus, the y-intercept is .
    In the graphs in the options above, we can see that graph B) has x-intercept less than 1 and y intercept -2.
    The x-intercept that we found above is 2 over 3 which is less than 1.
    Thus, the correct option is B)

    Note:
    We can also solve this question by eliminating the options.
    The first option A) is not correct because the line passes through the origin and so it must satisfy the equation, which is not true as 0not equal to- 2
    Then C) is not correct as the line passes through (0, -3), but this point does not satisfy the equation. Similarly, for option D) the point (0, 2) lies on the graph, but does not satisfy the equation.

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